Tony Abbott has accused political leaders of not doing enough to promote "Australian values", claiming that a "cultural cowardice" at the heart of public institutions such as the ABC and the public service has caused many voters to turn their backs on the major parties.

In the former prime minister's first substantial contribution to the so-called culture wars sparked by the Turnbull's government's decision to introduce a much tougher citizenship test for prospective immigrants, Mr Abbott argued mainstream political leaders had failed to promote the "virtues and benefits" of Western civilisation including "Gospel values" and free speech.

Former prime minister Tony Abbott is pushing for reform of the NSW Liberal Party. Credit:Alex Ellinghausen

"Whether it's official persecution of Queensland students for a bit of justified sarcasm, state governments promoting gender fluidity programs in schools, or a federal government-approved activist being disrespectful of Anzac Day, there's this pervasive ambivalence verging on hostility to our country and its values from people who should know better," Mr Abbott said on Wednesday night.

"Overwhelmingly, our people believe in our country – but it's hard for them to have faith in politicians when the politicians and those they promote don't believe in the things they do."

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Mr Abbott's outspoken criticism of Malcolm Turnbull's performance since the July 2016 election has dogged his successor, who is in the midst of trying to recast his government ahead of next week's federal Budget. Mr Turnbull has announced the government will build a Western Sydney Airport, and unveiled $19 billion in funding for Australian schools in a bid to secure the political middle ground.

Last month, he announced would-be Australians will face tough new hurdles – including a new English language requirements, a four-year probation period and an "Australian values" test – under a major shake-up of the migration program.

Mr Abbott has previously described the Coalition as being "Labor lite" and suggested his own party was "drifting to defeat". His latest intervention has promoted some observers to predict he will oppose aspects of Mr Turnbull's education funding reforms - which will leave about 350 Catholic and private institutions worse off - on the basis it will alienate core Liberal Party voters.

While he does not single out the government's handling of the debate over Australian values for explicit criticism in his latest comments, Mr Abbott does make it clear he believes Mr Turnbull should be making a more robust contribution to the culture wars.

"When the head of the Department of Prime Minister and Cabinet thinks that his decisions may have been tainted by 'unconscious bias', when the newly appointed ABC chairman thinks that his organisation has no objectivity problem, when dozens of big companies are more ready to campaign for same-sex marriage than for economic reform, when shareholder activism has intimidated big banks against investing in coal, and when it's all-but-impossible to discuss race, gender or religion in our universities without 'trigger warnings', the long march of the left through our institutions is almost complete," he said.

Pointing to the large numbers of voters who have turned their backs on the Coalition and Labor in recent elections, Mr Abbott said the gulf between "insiders and outsiders" needed to be closed by the political establishment paying more attention to values.

"If you are an Australian, you have to believe in Australia," he said. "This is what most of us believe. But only some of those in authority believe it; and those that do, don't state it nearly often enough."

Mr Abbott said Australians were mostly concerned with "real world" problems such as job security, economic disruption and national security. However, he also argues that "values disruption" could be even more unsettling.

Mr Abbott also took aim at part-time ABC presenter Yassmin Abdel-Magied, who courted controversy with an Anzac Day Facebook post suggesting Australians should also remember suffering on Manus Island, Nauru and in Syria and Palestine.

"Of course she was wrong to claim that Islam was the most feminist of religions. Of course, you can express any opinion you like; but why is it that only some opinions get you sacked, or investigated by the Human Rights Commission?" Mr Abbott said.

"Still, an over-promoted, politically correct 26-year-old is merely the symptom of the cultural cowardice that's penetrated to the very heart of our institutions. While officialdom wrings its hands in nervous self-doubt about anything that might be labelled anti-youth, anti-women, anti-black or, perhaps worst of all, anti-Muslim, Australians show what they think of our country's knockers by turning out in ever increasing numbers and ever greater enthusiasm on Anzac Day."